when I carry a .22 in the woods it's my Ruger 22/45 (because that's the one I shoot the best/most). Like others have said - if you buy decent ammo .22 doesn't misfire all that much. For woods duty I keep it loaded with CCI minimags.
I'd think for woods duty you'd want a .22 loaded with something pretty hot anyway. If you're going to try to kill anything humanly with a .22, you might as well make it as easy as possible for yourself.

But even if it's loaded up with practice ammo it's not as if failures are all that common. I get maybe 2-3 per 1000 with the cheepo bulk packs, so figure a 0.25% of failure. The only time when odds like that are going to be unacceptable are if you're getting attacked, and anything in the woods that's going to attack a human isn't going to be slowed down much by a .22 anyway.